Singularities of the wave trace for the Friedlander model

2014/12/24 by de Verdiere, Yves Colin, Guillemin, Victor, Jerison, David · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1412.7592

Abstract

In a recent preprint, we showed that for the Dirichlet Laplacian Δ on the unit disk, the wave trace Tr(e^it√Δ), which has complicated singularities on 2π- ε< t < 2π, is, on the interval 2π< t < 2π+ ε, the restriction to this interval of a C^∞ function on its closure. In this paper we prove the analogue of this somewhat counter-intuitive result for the Friedlander model. The proof for the Friedlander model is simpler and more transparent than in the case of the unit disk.

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• On the L^∞ norms of spectral projectors on shrinking intervals: the cases of some spheres of revolution and of the Euclidean disk

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